The distance of closest approach of an α -particle fired towards a nucleus with momentum p, is r. If the momentum of the a-particle is 2p, the corresponding distance of closest approach is

Question

The distance of closest approach of an α -particle fired towards a nucleus with momentum p, is r. If the momentum of the a-particle is 2p, the corresponding distance of closest approach is (A)  (r/2)  (B) 2r (C) 4r (D)  (r/8)

Tardigrade Admin · Accepted Answer

p propto (1/√r) r propto (1/p2) Hence, (r1/r2)=( (p2/p1) )2 =( (p/2p) )2=(1/4) r1=(r2/4)

Q. The distance of closest approach of an $α$ -particle fired towards a nucleus with momentum $p$ , is $r$ . If the momentum of the a-particle is $2 p$ , the corresponding distance of closest approach is

$\frac{r}{2}$

2r

4r

$\frac{r}{8}$

$\frac{r}{4}$

$p \propto \frac{1}{r}$
$r \propto \frac{1}{p ^{2}}$
Hence, $\frac{r _{1}}{r _{2}} = (\frac{p _{2}}{p _{1}})^{2}$
$= (\frac{p}{2 p})^{2} = \frac{1}{4}$ $r_{1} = \frac{r _{2}}{4}$

Q. The distance of closest approach of an α -particle fired towards a nucleus with momentum p, is r. If the momentum of the a-particle is 2p, the corresponding distance of closest approach is

2r​

2r

4r

8r​

4r​

p∝r​1​ r∝p21​ Hence, r2​r1​​=(p1​p2​​)2 =(2pp​)2=41​ r1​=4r2​​

Q. The distance of closest approach of an $α$ -particle fired towards a nucleus with momentum $p$ , is $r$ . If the momentum of the a-particle is $2 p$ , the corresponding distance of closest approach is

$\frac{r}{2}$

$\frac{r}{8}$

$\frac{r}{4}$

$p \propto \frac{1}{r}$
$r \propto \frac{1}{p ^{2}}$
Hence, $\frac{r _{1}}{r _{2}} = (\frac{p _{2}}{p _{1}})^{2}$
$= (\frac{p}{2 p})^{2} = \frac{1}{4}$ $r_{1} = \frac{r _{2}}{4}$